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Question 1126126: Mr. and Mrs. Garcia have a total of $100,000 to be invested in stocks, bonds, and a money market account. The stocks have a rate of return of 12%/year, while the bonds and the money market account pay 8%/year and 4%/year, respectively. The Garcias have stipulated that the amount invested in the money market account should be equal to the sum of 20% of the amount invested in stocks and 10% of the amount invested in bonds. How should the Garcias allocate their resources if they require an annual income of $10,000 from their investments?
Answer by ikleyn(52855)   (Show Source):
You can put this solution on YOUR website! .
Let x be the sum invested in the money market.
Then the sum invested in stocks should be 5x, The the sum invested in bonds should be 10x, according to the condition.
The total investments equation is
x + 5x + 10x = 100000 dollars,
which gives
16x = 100000, and hence
x =  = 6250 dollars.
Thus the investments should be $6250 in money market; $6250*5 = $31250 in stocks and $6250*10 = $62500 in bonds.
Now, let us check the annual income. At calculated investments, it should be
0.04*6250 + 0.08*62500 + 0.12*31250 = 9000 dollars.
It shows that at given conditions the problem HAS NO solution.
Answer. The problem is over-defined; in other words, it has TOO MANY conditions that do not agree each other.
Therefore, at given conditions the problem HAS NO solution.
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